The exact quote in question is the following:
LEILA: And this is for my good? Do you mind if I say I still love you? You never told me if you had another name, Mister Spock.
SPOCK: (wiping away her tears) You couldn't pronounce it.
From 'This Side of Paradise' (TOS)
The Memory Alpha page for Spock indicates his full name is generally unpronounceable to humans. I would postulate that it's probably a Vulcan name which humans (or at least English speakers) cannot pronounce because they don't know how to pronounce that particular phoneme. We see this occurring in different languages with sensitive/critical periods required to learn how to pronounce a certain phoneme and, if that period passes without learning it, one will never pronounce that phoneme properly (I can't find a reference or think of an example off the top of my head, but I'm sure I read that in some authoritative source; if you can think of one, please let me know in the comments!)
Looking at the question, we need to establish some of Data's known limitations. We know he has difficulty whistling (established in TNG 'Brothers). I refer you this answer and this answer which indicates that Data has a speech box, allowing him to speak whilst his head was detached from his body.
Having such a unit, it suggests to me (and I should know ;P) that, if the speech box were programmed to produce the necessary phonemes, then it should certainly be possible for Data to pronounce Spock's other name, as well as the Traveler's name.